On some multivariate gamma-distributions connected with spanning trees

Any correlation matrixR can be mapped to a graph with edges corresponding to the non-vanishing correlations. In particularR is said to be of a “tree type” if the corresponding graph is a spanning tree. The tridiagonal correlation matrices belong to this class. If the accompanying correlation matrixR or its inverse is of a tree type, then some representations of the multivariate gamma distribution are obtained with a much simpler structure than the integral or series representations for the general case.